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Physics 321
Solutions for Midterm #4
December 5, 2003
1) A planet of mass m is orbiting a star of mass M in some distant galaxy (you may
assume that M is vastly larger than m). At a given instant in time, it is observed to be a
distance d from
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Physics 321
Solutions for Midterm #3
1) Two particles of mass M and m exert a force on each other. This force acts on the line
between the particles, and has a magnitude F = k / r 3 , where r is the distance between
the particles. M is much gr
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Physics 321
Solutions for Midterm #2
1) Assume the Earth is a uniform sphere of radius R and mass M. Consider an object
thrown vertically upwards from the Earths surface at velocity vo. Neglect any resistive
forces.
a) (20 pts) What altitude w
Physics 321
Solutions for Midterm #1
1) An artillery shell of mass M is fired with initial velocity vo and initial elevation angle
. At the highest point in its trajectory, the shell explodes into two fragments of mass m1
and m2. Initially, these two mass
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Physics 321
Solutions for Final Exam
1) A small blob of clay with mass m is dropped from a height h above a thin rod of
length L and mass M which can pivot frictionlessly about its center. The initial situation
is shown below. The blob strikes
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Physics 321
Solutions for Midterm #4
1) An insect of mass m finds itself on the surface of a disk that is rotating with angular
velocity about an axis at an angle from the plane of the disk. The bug is a distance r
from the axis, and moving di
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Physics 321
Solutions for Midterm #3
1) 40 pts. A bead of mass m slides on a frictionless helix. The helix has radius r, and
when the helix is at rest its vertical position is defined by z = k. The entire helix is
being pulled straight upwards
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Physics 321
Solutions for Midterm #2
1) 25 pts. An oscillator is driven by a force F ( t ) = Fo cos ( t ) . After transient motion
has become negligible, the position of the oscillator is given by:
Fo
x (t ) =
(
= tan 1
2
o
)
22
+ 4
2
2
cos
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Physics 321
Solutions for Midterm #1
1) You travel through a wormhole to planet in an alternate universe. Newtons Laws
still apply in the new universe, but there is no air resistance and gravity behaves
differently: the force of gravity is giv
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Physics 321
Solutions for Final Exam
1) 70 pts. Consider a thin disk of radius R with mass distributed uniformly across it, as
shown below:
x3
R
x2
x1
a) 25 pts. Find the principal moments of inertia (principal axes are as shown on the
diagra